Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl

Naoki Hamamoto; Futoshi Takahashi

doi:10.3934/cpaa.2020139

Article Contents

2020, Volume 19, Issue 6: 3209-3222. Doi: 10.3934/cpaa.2020139

This issue Previous Article Stability problems in nonautonomous linear differential equations in infinite dimensions Next Article Ricci curvature of conformal deformation on compact 2-manifolds

Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl

Naoki Hamamoto and
Futoshi Takahashi^,

Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

^* Corresponding author
^* Corresponding author

Received: May 31, 2019

Revised: October 31, 2019

Published: March 2020

The second author (F.T.) was supported by JSPS Grant-in-Aid for Scientific Research (B), No.19H01800

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Abstract

In this paper, we prove Hardy-Leray inequality for three-dimensional solenoidal (i.e., divergence-free) fields with the best constant. To derive the best constant, we impose the axisymmetric condition only on the swirl components. This partially complements the former work by O. Costin and V. Maz'ya [4] on the sharp Hardy-Leray inequality for axisymmetric divergence-free fields.

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Mathematics Subject Classification: Primary: 35A23; Secondary: 26D10.

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References

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